Rendiconti Lincei - Matematica e Applicazioni

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Volume 25, Issue 3, 2014, pp. 275–291
DOI: 10.4171/RLM/678

Published online: 2014-08-31

Extended thermodynamics of rarefied polyatomic gases and characteristic velocities

Takashi Arima[1], Andrea Mentrelli[2] and Tommaso Ruggeri[3]

(1) Nagoya Institute of Technology, Nagoya, Aichi, Japan
(2) Università di Bologna, Italy
(3) Università di Bologna, Italy

Extended thermodynamics of rarefied polyatomic gases is characterized by two hierarchies of equations for moments of a suitable distribution function in which the internal degrees of freedom of a particle is taken into account. To obtain the closed set of the field equations for the system with many moments and for an arbitrary entropy functional that includes degenerate gases, the entropy principle and maximum entropy principle are studied and the equivalence of these two methods is shown as in the well-established case of the monatomic gas. In addition the recent results of the present theory are summarized. On the basis of physical considerations, the truncation orders of the two hierarchies are seen to be not independent on each other. The equilibrium characteristic velocities of the emerging hyperbolic system of partial di¤erential equations are analyzed and compared to those of monatomic gases. Inspection shows that the lower bound estimate of the maximum equilibrium characteristic velocity valid for monatomic gases, which increases as the truncation order increases, is valid for any rarefied polyatomic gas.

Keywords: Extended thermodynamics, maximum entropy principle, rarefied polyatomic gas, maximum characteristic velocity, moments equation

Arima Takashi, Mentrelli Andrea, Ruggeri Tommaso: Extended thermodynamics of rarefied polyatomic gases and characteristic velocities. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 25 (2014), 275-291. doi: 10.4171/RLM/678